# Thread: Circle question

1. ## Circle question

If you draw a circle inside a square and the circle fits exactly inside the square, how many percents of the square does the circle cover?

I need an easy and understandable formula and the result too if possible. Thanks!

2. Originally Posted by Shandy
If you draw a circle inside a square and the circle fits exactly inside the square, how many percents of the square does the circle cover?

I need an easy and understandable formula and the result too if possible. Thanks!
A circle inside a square of sidelength $\displaystyle x$ has a radius of $\displaystyle \frac{x}{2}$.

Substitute this data into the usual formulae for the area of a square and the area of a circle. Then calculate the percentage of area covered.

3. ## Correct or not?

Is my result correct or not?

A perfectly fit circle inside a square covers 80% of the square.

4. Originally Posted by Shandy
Is my result correct or not?

A perfectly fit circle inside a square covers 80% of the square.
If the radius of the circle is $\displaystyle r$, then the sides of the square are of length $\displaystyle 2r$.

So the fraction of the square that is covered is $\displaystyle \frac{\pi r^2}{(2r)^2} = \frac{\pi}{4}$, which is about 0.78, so you are about right.